Question

Use Euler’s method with two steps to estimate y(1) if y(x) is the solution to dy dx = x + y, y(0) = 1. Write your answer in the form a b where a and b are integers.

Answer 1

Answer:

1.5

Step-by-step explanation:

The Euler's method is a common approximation method for the solution of differential equations. It can be used to obtain an approximate value of a given function. The Euler's formula is:

$y_{n} = y_{n-1} + hF(_{x_{n-1},y_{n-1}})$

Therefore, n =1 will give:

$y_{1} = y_{0} + hF(x_{0},y_{0})$

h is the step size and it is equivalent to $\frac{x_{1}-x_{2}}{2} = \frac{1-0}{2}=\frac{1}{2}$

$F(x_{0},y_{0}) = x_{0} + y_{0} = 0 + 1 = 1$

$y_{1} = 1 + (0.5)(0+1) = 1 + (0.5)(1) = 1 + 0.5 = 1.5$